Tradeoff between lag time and growth rate drives the plasmid acquisition cost

Conjugative plasmids drive genetic diversity and evolution in microbial populations. Despite their prevalence, plasmids can impose long-term fitness costs on their hosts, altering population structure, growth dynamics, and evolutionary outcomes. In addition to long-term fitness costs, acquiring a new plasmid introduces an immediate, short-term perturbation to the cell. However, due to the transient nature of this plasmid acquisition cost, a quantitative understanding of its physiological manifestations, overall magnitudes, and population-level implications, remains unclear. To address this, here we track growth of single colonies immediately following plasmid acquisition. We find that plasmid acquisition costs are primarily driven by changes in lag time, rather than growth rate, for nearly 60 conditions covering diverse plasmids, selection environments, and clinical strains/species. Surprisingly, for a costly plasmid, clones exhibiting longer lag times also achieve faster recovery growth rates, suggesting an evolutionary tradeoff. Modeling and experiments demonstrate that this tradeoff leads to counterintuitive ecological dynamics, whereby intermediate-cost plasmids outcompete both their low and high-cost counterparts. These results suggest that, unlike fitness costs, plasmid acquisition dynamics are not uniformly driven by minimizing growth disadvantages. Moreover, a lag/growth tradeoff has clear implications in predicting the ecological outcomes and intervention strategies of bacteria undergoing conjugation.


Model development
Overview of logistic model for constrained growth/lag relationship To model the ecological implications of the observed tradeoff between lag time and growth rate, we developed a consistent method to constrain growth rates by observed lag times (i.e., the presence of a tradeoff), or lack thereof, for use in all subsequent simulations. Specifically, individual clonal growth curves were fit using the modified logistic growth equation 1 : Here, ( ! and ! are taken to be the maximum growth rate and lag time for each i th individual clone, respectively, Ai is the maximum density per clone, and Ni is the log-transformed cell density, as described in Methods. Linear regressions were then used to correlate fitted lag times, ! , to their corresponding growth rates, ( ! , yielding the fits shown in Fig (S2) ) = 1.31 * ) − 12.39. To simulate intrapopulation heterogeneity (i.e., to simulate variability amongst individual clones belonging to a single genetically identical population), where applicable, simulated lag times were randomly and independently drawn from a lognormal distribution parametrized by the mean and standard deviation of experimentally collected lag times. Lognormal distributions were chosen based on the literature consensus of this distribution type best fitting lag times, which was consistent with our data 2,3 ; normal distributions produced qualitatively similar results. Growth rates were then calculated using this a priori parameterized slope, relative to the mean lag time and growth rate of the plasmid (constrained, below), or randomly drawn from a normal distribution with the mean and standard deviation equal to that from the data (unconstrained): ( ! − / ) + / (1 + / (0,1)) (constrained) (S4) ( ! = / (1 + / (0,1)) (unconstrained) where / represents the coefficient of variation associated with / and (0,1) corresponds to the standard normal distribution. As detailed below, this linear regression framework was subsequently used to implement the presence/absence of a tradeoff in various simulation scenarios.
Bootstrapping method to predict time-to-threshold from lag/growth tradeoff (Fig. 3b) To verify the presence and criticality of the lag/growth tradeoff in predicting heterogeneous transconjugant dynamics, we utilized a bootstrapping approach to capture our acquisition cost data. Specifically, we simulated various de novo plasmid-bearing populations, defined by unique { / , / } values. Here, we aimed to ascertain the likelihood that observed lag/growth tradeoffs (i.e., Fig. 3a) arose randomly or through numerical artifact, or rather if they are essential to accurately predict observed times-to-threshold. Since experimentally, we quantify acquisition costs by tracking individual clones grown independently on an agar plate, we used the logistic model above (Eq. S1) to simulate the growth of all clones in the population without direct competition. We generated 300 independent clones either with or without a lag/growth tradeoff (Eq. S3-4), and simulated their growth for 48 hours using Eq. S1. The predicted time-to-threshold (TTTP) could then be extracted from each growth curve using the same threshold as in experiments (0.8), and its dependence on growth rate was calculated based on a linear regression across all clones. This process was repeated 1000 times to yield a distribution of predicted TTT/growth rate regressions. In the constrained case, this distribution represents the pooled effects of the lag/growth tradeoff as well as intrapopulation variability; in the unconstrained counterpart, only intrapopulation variability is reflected. As described in the main text, we found that for all de novo populations with experimentally verified ) > 0, an unconstrained model lacking this tradeoff was unable to accurately predict the observed relationship between TTT and growth rate.
Statistically, in the absence of tradeoff, the observed slope fell outside the 95% confidence interval of the predicted slope distribution. Conversely, simulating the relevant tradeoff was sufficient to capture the experimental slope value (observed value within 95% confidence interval of predicted distribution) (Fig. 3b).
In other words, the tradeoff between lag time and growth rate was necessary to capture the experimentally observed TTT; variability within clonal populations was not sufficient to explain this relationship. Intuitively, in the absence of a tradeoff, clones that grow faster reach TTT sooner, as seen in the adapted case. However, this negative correlation is not observed in de novo cells, which would only be predicted with a growth/lag tradeoff.

ODE model development
Our data clearly shows that acquisition costs are primarily driven by lag time, rather than growth rate. Thus, to simulate the population dynamics of de novo and adapted transconjugants, and the implications of acquisition cost, lag time, and growth rate relationships, we used a simplified set of ordinary differential equations (ODEs) that describe clonal growth and competition: where ! = 0 if < ! , and ! = ( ! if ≥ ! . Here, ( represents the shared carrying capacity, ! is the maximum growth rate for each i th clone, and the initial population consists of J total clones. All model parameters can be found in Supplementary Table 4. Generally, de novo and adapted simulations differ primarily in the lag times, while their growth rates are the same ( Supplementary Fig. 3c). In all cases, simulations were run for 48 hours to ensure accurate calculations of growth rates from the resulting curves. All presented distributions and statistics of simulation-generated lag times, growth rates, and population fractions were calculated based on multiple independent iterations of the relevant simulation initiated from identical conditions. In a given iteration, each clone $..7 was assigned a lag time ! drawn from the corresponding lognormal distribution with a mean and standard deviation as listed in Supplementary were sufficiently low such that these cells contributed to carrying capacity effects experimentally, even if they are unable to grow. Specifically, we assume that all parents were at least 1000X higher in initial density than corresponding de novo cells, but had a growth rate and lag time equal to 0, as the presence of dual antibiotic prevented their growth. For example, in a simulation with 100 unique de novo transconjugants (i.e., J=100), 100 independent populations (i.e., equations) were each initiated from independent singles clone with uniquely defined parameters and an initial density of 100 cells. Therefore, the parent population was initiated with a density of 1000*100= 1e5 cells. This is consistent with our experimental data, where low initial dilutions with high parental densities inhibited any transconjugant growth; in contrast, at sufficiently high dilution, residual parental density was minimal, allowing transconjugants to grow ( Supplementary Fig. 6b). In all cases, 50 independent iterations of each simulation were run to obtain an estimate of variation in the dynamics as driven by the distributions; the averages and standard deviations are reported.
Tradeoff results in a density-dependent growth advantage ( Fig. 4b-c) To simulate intrapopulation competition (i.e., Fig. 4b-c), competitions of varying J number of initial populations (i.e., clones) were used, from ~30 to ~300,000, where each population was treated as a unique clone at time=0 with distinct parameters (x-axis in figure). Thus, heterogeneous populations of increasing size were simulated, and resultant growth rate captured. To capture the growth rate equivalent to that observed experimentally, the parameters setting the growth rates for each clone (E.g., Eq. S3-4) are not sufficient, as these values do not scale with the number of populations, J; that is, an observed growth rate may potentially be limited due to total density (i.e., carrying capacity effects) even if the underlying parameterized growth rates of individual cells is high. Thus, for each iteration, the clone that reached the maximum density after 48 hours was selected (i.e., the "winner"), and an observed growth rate and lag time for that clone were calculated using the logistic method, equivalent to our experimental approach. We note that the average growth rates used to generate initial variability were chosen to match experimental data; however, the observed de novo growth rate is confounded by variability in individual cells' time since conjugation; at any given time, even a phenotypically homogeneous population will contain cells that have yet to begin growing, thereby depressing the observed growth rate. The mean and standard deviation of winner growth rates from 50 iterations are presented; changing the underlying mean growth rate only shifts the curves up or down, but does not alter the qualitative trends ( Supplementary Fig. 6c). Specifically, growth rates for both R100-1 populations are set to 0.4, whereas de novo RP4 was set to 0.3, and adapted RP4 to 0.5. Finally, the variance in these simulations was chosen to be low to capture the clonal heterogeneity while remaining biologically feasible (0.002).
Intermediate acquisition costs confer a competitive advantage ( Fig. 4d-f) To simulate generic inter-plasmid competition (i.e., Fig. 4d-f), we used the same set of equations to simulate two sub-populations, each corresponding to cells carrying one of two plasmids. Parameters for clones in each sub-population were drawn from independent distributions using the same approach as described above, each centered around the mean for that particular plasmid. To investigate ecological outcomes (i.e., final population fractions) across all possible plasmid cost combinations (i.e., Fig. 4d), we simulated pair-wise competitions between two populations: a reference plasmid, and a second whose cost was varied ( To simulate specific experimental competitions, as opposed to the range of lag times described above, we used specific parameter estimates based on the corresponding plasmids. Specifically, we first simulated competition between adapted sub-populations; their initial densities were scaled to ensure that they reached equivalent population fractions after 48 hours of growth ( Supplementary Fig. 8), in line with experimental observation. These initial conditions were then used as the starting densities for de novo competitions, with the lag times and slopes modified accordingly (Supplementary Table 4). Thus, any growth (dis)advantages enjoyed/suffered by de novo populations were easily distinguishable. We note that for these simulations, we used a higher variance to better capture inter-population dynamics (0.1, Fig. 4e-f); however, this did not impact the overall results, and the same variance as in all Figure 4 simulations can be used ( Supplementary   Fig. 9).  Supplementary Table 1c. The reported p values are calculated using a Bonferroni-corrected two-sided t-test. In all cases, TTT is defined as the time in hours it takes a bacterial population to reach a 'threshold' density in exponential phase. All Source Data are provided as a Source data file.  Supplementary Table 1c. B. Acquisition cost trends maintained using alternative growth rate quantification. Same trends as in Fig. 2b were maintained using the manual growth fitting method. P-values are reported for the slope of the linear regression. Each individual marker represents the mean lag time (or growth rate) and acquisition cost for all n colonies of a particular plasmid (Red: R100-1; Orange: R64drd; Chartreuse: R702; Green: RIP113; Mint: RN3; Light blue: RP4; Dark Blue: pB10; Purple: pOX38; Pink: pRK100). In all cases, colonies are pooled across at least three independent biological replicates (see Supplementary Table 1c for all sample sizes), black lines represent the linear regression line of best fit, and the R 2 and p values are reported. C. Instantaneous growth rate. Adapted (purple) and de novo (yellow) colony sizes were determined by averaging the pixel number for all colony replicates within a single plasmid, and the instantaneous growth rate (hours -1 ) was calculated by: log(x(t)/x(t-1))/0.25, where x is the number of pixels at time t. Colony numbers are the same as those reported in Fig. 2b. All Source Data are provided as a Source data file.

Supplementary Figure 4: Acquisition cost results are independent of the recipient selection agent.
Acquisition costs of plasmids R100-1 and RIP113 using the recipient strain RB933 were measured under tetracycline/kanamycin selection instead of tetracycline/rifampicin. Left: for the R100-1 plasmid, the TTT in hours (y-axis) of de novo (n=71, yellow) and adapted transconjugants (n=46, purple) plotted as a function of either growth rate in hours -1 or lag time in hours (x-axes). Right: for the RIP113 plasmid, the TTT in hours (yaxis) of de novo (n=35, yellow) and adapted transconjugants (n=62, purple) plotted as a function of either growth rate in hours -1 or lag time in hours (x-axes). In all cases, each marker corresponds to the TTT of an individual colony; bar height represents the mean TTT of at least two biological replicates. Black lines represent the linear regression line of best fit for each population; acquisition costs, Pearson correlation coefficient (r) values, and p values are reported for the slope of the regression line. All Source Data are provided as a Source data file. Only when the background population is sufficiently diluted is there room for de novo transconjugants to grow. Given day to day variation in transconjugant numbers, the primary source of variability arises in the diluted wells at lower cells density; therefore, experiments were done in technical triplicates from a single biological replicate. C. Growth rate does not change qualitative biphasic trends. Intrapopulation heterogeneity results for the RP4 plasmid (Fig. 4b) are independent of the de novo growth rate (hours -1 ). Marker color from gray to dark yellow indicate growth rates from 0.2 to 0.6 (main figure is 0.3), and black arrow indicates direction of increasing growth rate. Error bars represent standard deviations determined from n=50 iterations. All Source Data are provided as a Source data file.

C. Adapted RP4 and R64drd at varying initial ratios. Adapted transconjugants of intermediate-cost
plasmid RP4 (blue) and low-cost plasmid R64drd (red) were competed at the following ratios, with each ratio representing the relative amount of cells containing RP4 and R64drd, respectively: 1:1, 1:2, 1:4, and 1:20 (left to right). D. Adapted RP4 and pB10 at varying initial ratios. Adapted transconjugants of RP4 (blue) and pB10 (green) were competed in a 1:1 ratio representing RP4 and pB10, respectively. For both C-D, each plasmid's population fraction percentages were calculated by dividing the CFU from each unique drug plate (i.e., carbenicillin/rifampicin for RP4 and streptomycin/rifampicin for R64drd and pB10) by the total CFU from tetracycline/rifampicin, multiplied by 100. Each competition was conducted with n=3 biological replicates; each marker represents a unique biological replicate with each bar height representing the average of all biological replicates. All plasmids are in recipient strain BW25113-rif. All Source Data are provided as a Source data file.  B. Correlations between acquisition cost and distance between TetA and oriT/C. Distance between oriT(C) end nucleotide and tetA start was calculated, and correlation based on linear regression is reported (bottom row). rifampicin/tetracycline Fig. 2a-d, 3a-b, 4a Supplementary Fig. 2, 3, 6a